question_answer 1)

Determine if f defined by  is a continuous function.  

Answer:

For x < 0 and x > 0, f (x) = x2 sin , f is product of a polynomial and sine function.       Since polynomial and sine functions are continuous function.       Therefore f is also continuous.       At x = 0             As  and is bounded function between ?1 and 1.             and g (x) is bounded function.       Also f(0) = 0       Since        is continuous at x = 0       Hence f is a continuous function.